Catalysts comprising palladium and a support material are known catalysts for dienes and/or alkynes hydrogenation. Even though these catalysts are effective hydrogenation catalysts, some such catalysts tend to produce green oil by oligomerizing the alkynes and dienes. The green oil has 6 or more carbons per molecule and is not desirable in the production of an alkene such as, for example, ethylene because it fouls the catalyst and cuts the yield to alkene. Therefore, there is an ever present need for further improvements of a selective hydrogenation process to achieve enhanced selectivity to monoolefins, or increased catalyst life, or both. Accordingly, development of a modified supported palladium catalyst composition and its use in processes for the selective hydrogenation of diolefins (alkadienes) or alkynes to monoolefins (alkenes) would be a significant contribution to the art.